Base ten blocks are a mathematical manipulative that use different geometric shapes to symbolize place value powers of ten:

Unit | Ones (unit cube) |

Long | Tens (ten units long) |

Flat | Hundreds (ten units long, ten units wide) |

Large cube | Thousands (ten units long, ten units wide, ten units high) |

Base ten blocks are used for interactive visual learning of various number and place value concepts. Learners can easily see that ten of one type of block makes one of another. The size and spatial relationships between the various base ten blocks facilitates understanding of place value concepts. Students understand that it takes ten of one place value (or block) to make one of a higher value. Working with base ten blocks helps students understand regrouping in addition and subtraction.

Base ten blocks are often used with place value charts. This helps students organize their thinking and group blocks according to place value.

Virtual manipulatives, such as Brainingcamp's Base Ten Blocks Manipulative, let users stack base ten blocks and then automatically transform a stack of ten similar blocks into a higher value type (or break a block into ten of a lower value type). The Brainingcamp Base Ten Blocks Manipulative also supports decimals with blocks that represent tenths (0.1), hundreds (0.01) and thousands (0.001). To help students connect the standard symbolic representation of addition and subtraction, as blocks are moved the virtual manipulative automatically updates the symbolic sums and difference equation.

Using Base Ten Blocks

Place Value

Using a place value chart, place 12 ones cubes into the ones column. Combine 10 ones cubes to create a tens rod. Drag the tens rod to the tens column. The number 12 can be thought of as 1 ten and 2 ones. Add 8 more rods to the tens column to make the numbers 92. Add one more rod and combine the 10 tens rods to create a hundreds flat. Drag the hundreds flat to the hundreds column. The digits in each place value represent the amount of ones, tens, hundreds, or thousands in a number. The number 102 has 1 hundreds, 0 tens, and 2 ones. Each place value represents 10 times as much as each lower place.

Comparing Multi-Digit Numbers

Using a Place Value Chart, model the number 43 at the top of the chart and the number 37 at the bottom of the chart. To compare which number is greater, compare the greatest place value (the tens place). The number 43 has more tens than the number 37, so 43 is greater than 37. The comparison can be written with an inequality symbol as 43 > 37. When the numbers have the same digit in the greatest place value, compare the next greatest place value.

Multi-Digit Addition (No Grouping)

To add 13 and 35 using a place value chart, model 13 at the top of the chart 35 at the bottom of the chart. There are 4 tens and 8 ones in total, so 13 + 35 = 48.

Multi-Digit Addition (With Grouping)

To add 17 and 8 using a place value chart, model 17 at the top of the chart and 8 at the bottom of the chart. Start by adding the ones. If there are 10 or more ones in total, combine 10 ones to create a ten. Drag the ten to the tens column. There are 2 tens and 5 ones in total, so 17 + 8 = 25.

Subtraction (No Grouping)

To subtract 13 from 48 using a place value chart, model 38 at the top of the chart and 13 at the bottom of the chart. Model subtracting by combining red and green cubes to create zero pairs. When there are no more red objects remaining, there are 3 tens and 5 ones in total, so 48 - 13 = 35.

Subtraction (With Grouping)

To subtract 8 from 25 using a place value chart, model 25 at the top of the chart and 8 at the bottom of the chart. Starting in the ones column, model subtracting by combining red and green cubes to create zero pairs. Since there are not enough green ones to create zero pairs with all the red ones, regroup 1 ten as 10 ones by dragging a green rod from the tens column to the ones column. Continue subtracting by combining red with green ones. When there are no more red objects remaining, there are 1 tens and 7 ones in total, so 25 - 8 = 17.

Introducing Decimals

Using a decimal place value chart, place a ones cube in the ones column. Now drag the ones cube to the tenths column to its right. Notice that each tenth is 1/10 of a one. Numbers that have digits in place values smaller than the ones place are called decimals. Drag a tenth to the hundredths place to see that 1 hundredth is 1/10 of a tenths (or 1/100 of a one). Delete 1 hundredths rod. The base ten blocks represent the decimal 0.99 because there are 0 ones, 9 tenths, and 9 hundredths.

Comparing Decimals

Using a decimal place value chart, model the number 2.08 at the top of the workspace and the number 2.1 at the bottom of the workspace. To compare which number is greater, start by comparing the digit in the greatest place value (the ones place). Since the ones digits are the same, compare the next greatest digit. In the tenths place, 1 is greater than zero, so 2.1 > 2.08.

Adding and Subtracting Decimals

Adding decimals is similar to adding whole numbers. Using a place value chart and starting with the smallest place value, add digits and regroup as necessary. To subtract decimals start with the smallest place value position and combine red and to green base ten blocks to create zero pairs, regrouping as necessary, until there are no remaining red blocks.